Add the potatoes and onion to a large pot.
Add water to cover the potatoes by 1 inch. Set on medium high heat. Cook until the potatoes are fork tender, stirring occasionally.
While the potatoes are cooking, take the sliced ham and set the entire stack on a cutting board, then cut into ½ strips. Once you have the stack cut into strips, just turn the cutting board 90 degrees then then cut the strips crosswise into ½ inch cubes, there, the stack of ham is now diced. Using sliced ham allows more ham to be distributed throughout the soup.
When the potatoes are tender, reduce heat to low. Scoop out some of the water so the water is just at the top of the potatoes, reserve the water to add if needed if you want a thinner consistency. Now add the soup, ham, and cheese, stir together.
Simmer until the cheese is melted and the soup and cheese is mixed in well. Season with salt and pepper as desired. Stir in some of the reserved potato water if you want thinner soup.
Ladle into bowls, serve, and enjoy.